$(12$ pts$)$ Construct a DFA for the language, L $-\{$A language of binary strings that neither ends with $\text{'}10\text{'}$ nor $\text{'}01\text{'}\}.$

Deliverables:

$($a$)$ Construct a $($minimal$)$ DFA for the following language, L $-\{$A language of binary strings that ends with either $\text{'}10\text{'}$ or $\text{'}01\text{'}\}.$

Draw the DFA.

$($b$)$ Now construct a DFA for the following language, L $-\{$A language of binary strings that neither ends with $\text{'}10\text{'}$ nor $\text{'}01\text{'}\}.$

Use the algorithm for finding the DFA for the complement of a regular language, along with the DFA you created in the previous step.

Draw the DFA.